if you live in France and work in Switzerland, you will have a french insurance. it is called "assurance pour frontaliers". Because it is a french insurance ... that has to comply with the Swiss law (lamal).
There you can insure every member of your family.
free quote
I don't know these people ... it is simply for the sake of helping you that i provide you this link. Since they have no english page, in case you do not understand ... google translate ... et hop !
i still encourage you to ask for another quote in another place ... google.fr ... then you copy paste : "assurance maladie pour frontaliers en suisses".
and pages of solutions will appear !
isn't technology nice
I am insurer in Switzerland ... therefore their is nothing else i can do you for ... unless you really need more help ... and i can give you contact people in France.
Don't worry, it is very common and you will soon understand everything you need thanks to some well explained sites that you will find under this google.fr page.